Mathematical modeling and Bayesian estimation for error-prone retail shelf audits

• This paper is motivated by the practical need of retail shelf audit service providers.
• We derive static analytics under risk neutrality and conduct simulation analysis under risk aversion.
• We discover interesting dynamics among inspection error, cost factors, shelf failure rate, and optimal decisions.
• We show that managers’ risk preferences do have substantial impacts on optimal decisions.
• We propose a Bayesian statistical model and a Markov chain Monte Carlo approach to estimate unknown model parameters.

Prevalent execution errors such as out-of-stock, inventory record inaccuracy, and product misplacement jeopardize retail performance by causing low on-shelf availability, which discourages not only retailers who have lost sales but also manufacturers who have worked hard to deliver goods into retail stores. Thus, external service companies are hired by manufacturers to conduct manual inspection regularly. Motivated by the practical need of shelf audit service providers, we use a general cost structure to develop a decision support model for periodic inspection. Some qualitative insights about the intricate relationships among inspection efficacy, cost factors, failure rate of shelf inventory integrity, and optimal decisions are derived from analytics assuming risk-neutrality. From simulation experiments we also find that managers' risk preferences have non-trivial impacts on optimal decisions. Based on a total cost standpoint high-quality inspection is predominantly preferred regardless of the level of risk aversion. Finally, we propose a Bayesian statistical model and a Markov chain Monte Carlo approach to estimate model parameters such that managers can make empirically informed decisions. Our major contribution lies in developing a mathematical model that is practically applicable and proposing a Bayesian estimation approach to rationalize unobservable model parameters, which are influential to optimal decisions but often arbitrarily assumed by decision makers.